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Please consider a standard horizontal spring mass oscillator system (with no friction).

When doing SHM physics problems I would assume energy is conserved. However, I never got why it was conserved.

If you consider the spring and the mass itself to be the system, why doesn't the force from the wall (which the spring is attached to) do any work? Does that mean the wall is considered part of the system (making the force an internal force?)?

If the wall isn't considered part of the system, then wouldn't it mean momentum in $x $ direction isn't conserved either (net external force from wall)?

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If you consider the spring and the mass itself to be the system, why doesn't the force from the wall (which the spring is attached to) do any work?

$W=\vec F \cdot \vec d$. The displacement of the force from the wall is 0. Since the displacement is 0 the work is 0 regardless of the force.

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  • $\begingroup$ Does that mean energy is conserved but momentum isn't? $\endgroup$
    – AwesomeGuy
    Commented Jan 17, 2021 at 2:06
  • $\begingroup$ Correct. There is an external force so the system’s momentum is not conserved $\endgroup$
    – Dale
    Commented Jan 17, 2021 at 2:08
  • $\begingroup$ Also, why is the displacement 0? Doesn't the CM of the spring itself move during SHM? $\endgroup$
    – AwesomeGuy
    Commented Jan 17, 2021 at 2:10
  • $\begingroup$ The wall doesn’t move. Specifically, the part of the wall touching the spring does not move. $\endgroup$
    – Dale
    Commented Jan 17, 2021 at 3:14

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